This invention relates generally to polyphase code systems and more particularly to digital systems for coding and decoding sequences of polyphase encoded systems.
In a conventional radar, the transmitted waveform is a train of pulses as shown in FIG. 1a of the accompanying drawing. The mean power is determined by the peak power and the duty ratio, that is to say the ratio of the width of the pulses to the overall repetition period T.T. is fixed by the maximum unambiguous range, and the .tau. by the resolution required. Thus, to improve the detectability of the radar only the peak power can be increased and this is limited by the components used. There is therefore a confict of interest if both improved detectability and resolution are required.
It is now recognized that the resolution is not governed by the pulse length but by the overall transmitted bandwidth. Thus, by modulating the carrier within the transmitted pulse length the bandwidth is increased and the resolution improved with no reduction in mean transmitted power.
One known form of modulation to effect pulse compression is phase modulation in which, within the width of the transmitted pulse, the phase is changed at specified intervals or subpulses. While these phase changes can follow a random sequence, by using certain well-defined sequences known as "Frank Codes" it is possible to reduce the level of the sidelobes after processing of the received pulse. An example of a known method to transmit and detect Frank-coded radar pulses is described in U.S. Pat. No. 4,237,461.
In FIG. 1(b) of the drawings, there is shown the pattern of phase changes within a pulse 11 subdivided into four phase groups of subpulses 11 a-d, each phase group having four subpulses .tau. seconds long, so forming a Frank code with a pulse compression ratio of (4).sup.2 =16. The subpulses are at a constant carrier frequency and related to a CW reference signal by a phase angle of (n)(90.degree. ), where 0.ltoreq.n.ltoreq.3. The phase, in radians encoded on each of the subpulses 11a-d of the pulse 11 may be determined from the matrix of Table 1, as read from left to right progressing from the top to the bottom row.
TABLE 1 ______________________________________ 0 0 0 0 0 .pi./2 .pi. 3.pi./2 0 .pi. 0 .pi. 0 3.pi./2 .pi. .pi./2 ______________________________________
A clockwise phase rotation (phase delay) has arbitrarily been assigned a negative value while a counterclockwise rotation (phase advance) is designed a positive value. A phase advance of X radians is equivalent to a phase delay of 2.pi.-X radians. This phase in complex numbers is shown in Table 2.
TABLE 2 ______________________________________ 1 1 1 1 1 j -1 j 1 -1 1 -1 1 -j -1 +j ______________________________________
The phases encoded on the four subpulses of the first phase group 11a are indicated in the top row of the matrix of Table 1 or Table 2; the phases encoded on the four subpulses of the second phase group 11b are indicated in the second row of the matrix; the phases for the four subpulses of the third phase group 11c in the third row: and the phases for the four subpulses of the fourth phase group 11d in the fourth row. Examining the phases encoded on the the four subpulses of each phase group 11a-d, it will be seen that the phase increases linearly from subpulse to subpulse at a rate of 0 radians per subpulse in the first phase group 11a; at a rate of .pi./2 radians per subpulse in the second phase group 11b; at a rate of .pi. radians per subpulse in the third phase group 11c; and at a rate of 3.pi./2 (or -.pi./2) radians per subpulse in the fourth phase group 11d. Examining the slope of the phase increase of each phase group, it will be seen that the slope increase linearly from phase group to phase group at a rate of .pi./2 radians per phase group. Since frequency is the rate of change of phase, linearly increasing phase is a constant frequency. Thus, each phase group 11a-d represents a different frequency measured with respect to the carrier frequency, viz. 0, (.pi./2)/.tau., .pi./.tau., and (3.pi./2)/.tau. (or -(.pi./2)/.tau.) respectively for each of the phase groups in order. Since the frequency (slope of phase) also changes linearly by (.pi./2)/.tau. from phase group to phase group, the Frank code is seen to be a step-wise approximation to a swept frequency.
The auto-correlation function of pulse 11 as might be obtained in the matched filter of a pulse-compression radar receiver is shown in FIG. 1c. This graph shows the level of correlation of a pulse as in FIG. 1b with a similar pulse when plotted against the relative time of the pulses being completed. It will be seen that except at coincidence in time, the correlation function takes on values between 0 and 1 and that when the two signals are coincident the correlation function has a value of 16. This means that though the transmitted pulse has an overall duration of 16.tau., the resolution of the radar is 1.tau. and there is a ratio of 16 to 1 between the level of the sidelobes and the correlation peak.
One problem with the Frank Code has been an increase in the sidelobe level of the autocorrelation function due to the bandwidth limitations in radar receivers. This bandwidth limitation causes maximum attenuation in those phase groups with large shifts between adjacent subpulses. Note that for the 16 element Frank code the large shifts between adjacent subpulses occurs in the third phase group 11c. It has been determined that the increase in sidelobe level is a maximum when attenuation is a maximum near the center of the phase coded pulse and a minimum when maximum attenuation takes place near the ends of the pulse. Thus the Frank Code experiences a significant sidelobe level increase because the third phase group 11c (0.pi.0.pi.) is near the center of the pulse.
This inverse weighting disadvantageously suppresses the peak response of the radar receiver. It also reduces the ratio between the correlation peak of the autocorrelation function and the level of the sidelobes. This reduction is undesirable because it increases the possibility that weak target echos will be hidden by the sidelobes from an adjacent stronger target echo.
In order to lower the sidelobe level of the autocorrelation function various codes have been developed with the phase changes ordered so the maximum phase shifts occur near the ends of the pulse. In particular in U.S. Patent Application No. 65,456, filed 8-10-79, now abandoned by F. Kretschmer discloses an apparatus including an N point FFT with N being an even integer and fixed phase shifters interconnected to generate a P1 coded pulse. The P1 coded pulse generated exhibits the desired low sidelobe level. However, the fixed phase shifters interconnected with the N point FFT is a relatively complicated and expensive structure.